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Патент USA US2407287

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SepìII E0, i946,
E. LABIN
EAW/,287
COURSE BEACON
F‘i‘led June 28, 1941
2 Sheets-Sheet l
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BY
l
ATTORNEY
sep@ my ma
E. LABIN
2,407,2@7 '
COURSE BEACON
-Filed June 28, 1941
2 Sheets-Sheet 2
Patented Sept. l0, 1946
2,407,287
unirse srarss PATENT oFricE
2,407,287
COURSE BEACON
Emile Labin, New York, N. Y., assignor to Federal
Telephone & Radio Corporation, a corporation
of Delaware
Application June 28, 1941, Serial No. 400,259
14 Claims. (Cl. 250-11)
l
2
This invention relates to radio direction-indi
cating and direction-finding apparatus, and is
directed particularly to means for producing an
aircraft iiight beam of high accuracy.
It is an object of the invention to provide means
undetectable by the enemy, hence, relatively
secret. A pair of such beacons could be projected
thus very accurately define this desired location,
for producing an airplane course beacon of
greater directive accuracy and longer range than
which, say, it is desired to bomb. In order to
assure further secrecy these beacons could be
from spaced points within one territory to inter
sect at a desired location in another territory and
varied while the bombers are en route to their
has hitherto been attainable.
objective, and their intersection need only be
Another object is to provide an improved radio
beacon which will not give distorted and mislead 10 made to occur at the objective as the bombers
are immediately approaching. It would thus be
ing course information due to the presence of re
fleeting objects.
possible to bomb a ñxed target with relative accu
racy without requiring bombardiers to first see
A further object is to provide improved means
their targets.
'
for varying the directivity of an airplane course
In order to obtain increased accurate course
beacon at will.
15
range I propose to use pulse modulation trans
It is also an object to provide an improved
mission means in which a series of impulses of
course beacon that does not depend upon antenna
unusually high instantaneous power is trans
directivity for its accuracy.
mitted. To establish a course two transmitting
Other objects and various further features of
novelty and invention will hereinafter be pointed 20 antennas are each fed with energy of the same
out or will become apparent from a reading of the
impulse frequency
following specification in conjunction with the
drawings included herewith. In said drawings
Fig. 1 shows schematically a preferred arrange
ment and layout of transmitting and receiving 25 but displaced a certain interval of time bo, one
series with respect to the other. Along any line
apparatus in accordance with features of the
invention;
extending radially outwardly from the midpoint
between these antennas the time interval between
Fig. 2 is a graphical representation of energy
receivable pulses will be the same, and thus concharacteristics at diiierent positions in the layout
of Fig. 1;
30 stant, along that line or course.
Now, if an airplane carries receiving equipment
Figs. 3 and 4 are graphs illustrative of the op
responsive to the time displacement between suc
eration of the arrangement shown in Fig. 1; and
cessive impulses of both these series, it can be
Fig. 5 shows geometrical considerations involved
given an indication of any course to be followed;
in my novel course system.
The invention is concerned with improved 35 that is, the course may be determined by this time
interval. I consider it preferable, however, to pro
directing apparatus for indicating to an airplane
vide the receiving Sets responsive only to one pre
pilot a desired direction of flight with high accu
determined time interval and then to control the
I‘äCY.
time interval between pulses of both transmitting
This novel system contemplates a directive ar
rangement whereby angular directive accuracy 40 sources by appropriate phase adjusting means in
order to send the aircraft out on a fixed direct, or
improves with distance from the transmitter and
controlled indirect course.
a beam may be projected for distances hitherto
With this brief general introduction, the inven
unobtainable with accuracy. The system is at
tion> will now be described in connection with the
the same time further adaptable to changes in
directivity.
45 drawings. Fig. 1 schematically shows in block
diagram form elements of my novel beacon sys
Such a system will be appreciated as having
tem, including the transmission and receiving
very deñnite civil as well as military value. In
(airplane) stations. In the form shown the
commercial aviation there is a deiinite call for a
transmitting equipment includes a pair of an
course beacon having great accuracy and substan
tennas lil and II spaced preferably a substantial
tially unaiîected by large reflecting bodies, such as
distance apart for greater accuracy, as will be
clear. Antenna Il) is associated with transmitter
A, and antenna Il with transmitter B. Each of
these transmitters is supplied with a periodically
that may be readily followed and that is relatively 55 recurrent impulse signal spaced in time, one with
high mountains. The present invention will help
to ñll such needs.
From a military point of View it is considered
desirable to provide a sharply directive beacon
2,407,287
3
4
respect to the other. In a preferred form a single
no matter what the form of the impulses just
impulse generator l2 is employed for supplying
both transmitters, and in substantially the follow
ing manner. Generator l2 supplies impulse
energy directly to transmitter B. A receiving
antenna lli’ at station A is receptive to this im
pulse energy; and, after receiving the pulses in
receiver S and appropriately delaying the same
as long as they are short enough'.
From the Fourier formula the amplitude Am
for the mth harmonic of a single series of the
transmitted pulses over the period T is given as_
by time-delay means i3, the impulses are re
where f(t) represents the pulse shape.
A „f-TL
-2 Tf(t)
transmitted at A. A pulse displace indicator 2|
(l)
Now,
since',f(t)=0 for values of t between d and T,
the integral is limited by tzal. However, if d
is so small that for all reasonably small values
receives energy from the receiver 8 and from the
output of delay means i3 for comparison indi
cation, whereby the eiiect of the time delay means
i3 can be observed and monitored.
cos mot. d t
of m
If desired, a
cos mwd=l
receiver and monitoringr circuit 9 may also be
provided at B for ascertaining whether the delay
it is found that for all forms of f(t) if Vm is rea
between transmitted impulses from A and B are
spaced properly to denne a correct course.
sonably small
low, along any radial direction from the mid..
2 T
2 a
point between A and B, and particularly at 20
greater distances, received impulse energy will
that is, for all impulse forms the amplitude of
comprise a recurrent pattern of two pulses, spaced
the lower harmonics is equal `to the mean value
in time according to the radial direction. Since
of the periodic function fût). Thus for a single
any such pulse pattern will have a definite har
monic make up, I propose to employ harmonic 25 series of pulses all low harmonics have the same
analysis
the receiver to give the course indi
amplitude.
cation to the pilot. Accordingly, a preferred form
In the case of a double pulse series, however,
the different low harmonics will have diiîcrent
of receiver comprises radio and intermediate fre
amplitudes. The amplitudes of the various har
quency stages it, and limiting and detecting
means, l5 and iS, respectively, After detection 30 monics forming the received complex double pulse
series will vary simply as cos mwb. This will be
of the two-pulse signal, for purposes that will
clear by considering one series of pulses, say
later become apparent, I propose to identify by
appropriate ñlter means il, I8, le, and 2Q various
from A, as»
odd-harmonics of the signal in addition to the
Am--Q-,L f(t).cos mwtdt-îfûfuydt
fAo) :EAW @es mwa
fundamental and an even harmonic. Informa
tion acquired from a dii'îerential indication of
various voltage outputs of these ñlters may give a
direct indication as to whether the desired course
(2)
(s)
and the other, say from B, as
fßw =ZA,„. COS mwc- b)
<4)
is being followed.
Fig. 2 shows schematically the energy output 40 The combined result of these signals, represent
of the respective transmitters and the kind of
ing received energy will be
energy received at the craft that is being guided.
Pulses of the same period T are transmitted at
b
QU) :ZZAW 00S mgb'
A and B and are time-displaced from each other,
as so adjusted by the phasing control I3. In
transmission from A to the receiver there will
cos mw t-î
(5)
Since the term 2Am is clearly not dependent on
the value of b, and since the term
be a certain delay TA, and another delay rs as
sociated with energy coming from B. If the in
terval between the radiation of a pulse from
cos mw
(il)
2
A and the radiation of the corresponding pulse 50
from B is bu, the -total displacement between
will vary periodically between +1 and -1 n0
pulses at the receiver will be b, the resultant of
matter what value is chosen for b it is clear that
controlled and transmission delays-bo-rA-l-TB.
the term cos (l/gmwb) is the sole term deñning
We shall new analyze the received signal, two
the relation of the absolute magnitude of the
pulses displaced by an interval b.
received energy for any harmonic to the dis»
It may be shown from a harmonic analysis
placement b between pulses.
of the received signal g<t> that all frequencies
Fig. 3 is a series of graphical representations
showing how the magnitude Ym of this
which are multiples of
60
will have phase and amplitude characteristics
dependent upon the delay of one series with re~
spect to the other, that is, upon the magnitude
of b. The phase variation may be neglected
since the detected harmonics are used only to
give currents proportional to the magnitude oi
their amplitudes. Furthermore, since only lower
order harmonics are to be considered, it will
be assumed that the duration d of the impulses
is small enough for the amplitude of the Various
harmonics of each series to be independent of
the harmonic order. As will be shown in the
csmwb
o
2
term varies for a number of the lower order h'armonies when b is considered for Values of zero
to
T
2
It will be observed that all of the odd-order har
monic curves intersect and are thus equal for a
delay b of
T
following paragraph, this assumption is valid 75 between received impulses. Those odd harmonics
5
2,467,287
6
of the orders 4m-l-1 (m being zero or any whole
number) will vary with b about
indications for more courses than the true one
T
4
In order to eliminate the error of following a
false course I propose to employ some additional
indication of the value of an even harmonic, say
as a cosine function varies about
the second, which passes through zero only at
4
T ,
b-r
that is, with a negative slope; and the odd har 10
monies of orders 4m-l-3 will vary with b about , Thus, by simultaneously following the second
T
4
harmonic zero and a zero of one of the §-Curves'
a pilot will be “on course.”
ItA will further be observed in connection with
as a sine function varies about
15 Fig. 4 that differential curves for higher order
harmonics (e. g. §35) are of steeper slope at
4
T
that is, with a positive slope. It will be seen,
4
then, that two odd harmonics of successive order
than lower harmonics. This steeper slope may
20
may be used to define an axis about
be utilized as the correct course is approached to
T
give higher magnitude indications in the “on
4
course” neighborhood of
In accordance with features of my invention I
b: Z
4
use two such successive harmonics to obtain a 25
and thus to follow the course still more accu
differential indication of their relative magni
rately. On the other hand, when considerably
tudes.
“off course,” it may be desirable to employ lower
In Fig. 4 I show graphically the resultant curves
obtained from differential Superpositions of such
order harmonic differentials (e. g. §31) to elimi
30
nate false zeros and to be able to follow down
successive odd harmonics of the received signal
only one slope to get "on course.” It thus ap
pattern. In this figure, curve §31 represents a
pears preferable toy use the §31 and
quantity proportional to the diiïerence between
the third harmonic and the fundamental, and
§35 the third and fifth' harmonic differential. An
indications when the receiver plane is far from
even harmonic, in the present instance the sec
the axis, and §35 or §51 when in the neighborhood
ond Y2, is also shown, as it is employed for pur
of the axis. If b is permitted to vary only within
poses that will be later pointed out.
relatively small, limits about Y.
It will be noted in connection with the curves
'
`
l'
of Fig. 4 that both the differential curves vary
in the same sense either side of a norm, where 40
4
then the §31 curve may be employed merely for
b
quadrant identification purposes. Since the
maximum variations of b about
When time-displacement b of received impulse 45
vT
patterns is greater than
4
T
4
(when bo has the value ë)
odd-harmonic differential energy will have posi 50 are determined by D, _the transmission time be
tween A and B, variation in b may readily be kept
tive values; and when these differentials are less
do-wn to a small fraction of T by appropriately
than
selecting the pulse period T sufficiently large
4
resultant energy is negative.
It thus appears
with respect to the distance between transmitters
55 A and B.
Referring to the elementary diagram of Fig. 5,
I show the geometrical considerations involved
in rotating the direction of the course
that if a flight course be determined by a differ
ence b between pulses equal to
T
4
a receiver adapted to ñlter out harmonics and
compare differentials as above-indicated will
have zero output whenever the receiver is exactly
60
without physically displacing antennas I0 and
l l. Assuming for the moment that bo is
4
“on course.” Drift to one side will give rise t0 65
too large a differential with resultant positive
it is clear that unless the receiver is “on course,”
§-output, and the converse will hold for drift
the detected pulse time displacement b will not be
“off course” in the opposite sense.
T
Of the many indicating means that will sug
4
gest themselves to the reader, I prefer to employ 70
a voltmeter giving visual indication of positive
but rather some other value equal to
or negative harmonic differential voltage values.
In a practical application of this indication sys
tem it will be seen that by using only the y or
differentia1 curves, it is possible to obtain zero 75 (r being the differential ril-rs, see Fig. 2).A
' moms?
8
7
Now, if a designates the angle of OM (i. e. a
line joining some point between transmitters A
and B to the receiver) measured clockwise from
the reference line XOX’ (perpendicular to a line
between transmitters A and B) then for values
of the distance OM very much greater than the
distance AB,
sin
OC:
T
error in the B sector and 0.40o in the A quadrant.
Although I have described my invention in
connection Iwith the preferred forms illustrated,
it is to be understood, of course, that many modi
fications will fall within its scope. For example,
if it should be deemed inexpedient to provide the
impulse generator l2 feeding both transmitters
A and B by the method shown, a transmission
line arrangement could be employed.
In this
D
10 case generator i2 could feed both transmitters
where D as above-indicated is the transmission
A and B, simultaneously and directly. The above
time between A and B. A condition precedent to
described delay means could then be provided in
being “on course” is that bo, the delay instituted
the transmission line intermediate the pulse gen
at the transmitters by the delay means I3, plus
erator and one of the transmitting stations. A
the transmission delay r be equal to
15 monitoring circuit also similar to the one above
described could be employed for the same 'stand
T
ardizing purposes by disposing it so as to com
4
pare the delay between impulse energy fed to
In order, then, to denne a bo that will produce
both transmitters.
or set up a course at a desired angle an with the
It is further clear that the invention is not to
perpendicular XOX’
be considered limited to the particular order har
monics described. For example, higher odd har
T
monics than the iifth may be employed for even
Tho
In other words, to rotate the direction axis an '
angle an clockwise from the perpendicular, the
time between pulses at the transmitter must be
greater course accuracy inasmuch as the higher
the harmonic order the closer a t peak ap
proaches the true course, and the steeper this y
curve’s slope at
b: l"
4
30
Although other even harmonics may be employed
To this end, the delay means i3 may be used
for the true-course check as above indicated, it
to control bo and appropriate monitoring and
is preferred that the second be employed, for this
indicating means 2l provided for accurately ob
harmonic has the property of only reaching Zero
serving and. Calibrating course directivity. For
once in the entire interval from
purposes of easier calculation and design I prefer
to employ a spacing between stations A and B
b=0 to b=g
such that the interstation delay D will be some
integral sub multiple of the interval
Ii a limiter of known construction is employed
in conjunction with received energy only the
T
40 stronger signals, i. e. the impulse energy, will be
4
eñective as to the rest of the receiver. In this
Since the variation in r incurred in rotating
way it Will be possibile to eliminate Very substan
the course axis from OA to OB (i. e. from a posi
tially any reflection or other disturbing eiïects
tion 90° on one side of XOX’ to a position 90°
due to terrain irregularities, as will be clear.
on the otherv side of XOX’) is 2D, the minimum 45 Furthermore, since the maximum amount of the
value of
impulse displacement that need be used in ac
cordance Iwith the invention is within
T
4
T
2
is determined by 2D. Thus
The signal-to-noise ratio in the receiver may
T
further be increased by half-wave rectifying
should equal at least 8 for complete rotation of
the course (180°).
When the course coincides
with XOX’, i. e. when the delay
some of the output energy, say from the funda
mental filter l?, and employing this rectiiìed en
ergy appropriately to control a blocking signal,
as more fully disclosed in my copending U. S. ap
plication Serial No. 385,282, ñled April 1, 1941.
It is further to vbe observed that in addition to
the peak-to-zero amplitude variation of §35 repre
sents approximately a fifth of the interval
T
presenting advantages inherent in pulse modu
lation, my novel directing system does not re
quire that antennas i0 and H be of any par
ticular directive nature. It is preferable that
4
they be of the same general form and charac
ter so as each to propagate in substantially the
in the B or right-hand quadrant, corresponding
to about 23° course variation in this sense. In 65 same manner, but they need not be of the di
rective type. If they are non-directive, it is clear
the A or left-hand quadrantl this amplitude vari
that courses of the same strength may readily
ation corresponds to a b decrement of a third
be set up in any desired direction without hav
of the
ing to make any physical adjustments or alter
T
70 ations in the antennas. A mere single manual
4
adjustment of the delay means I3 is all that is
interval-representing 40° angular displacement
needed.
that average precision for a 1% indication varia
t is also to be noted that although I have de
scribed an arrangement in which course control
tion in the §35 readings will represent 0.23o course
is eiîecterli at the transmitting end, means may
in that quadrant.
It would appear, therefore,
2,407,287
9
10
be provided whereby the pilot can set his own
course for any given relation of transmitted im
pulses. It is clear that to this end time delay
means effective to displace received impulses of
a double-pulse signal with respect to each other
may be provided at the receiver, and this phase
delay means may be adju-stable by the pilot. In
tiple frequencies for indicating a characteristic
of the received impulse energy.
this way if a single course were deiined by a
5. In a course beacon system, a receiver accord
ing to claim 4, in which said indicating means
includes means supplying the effective energy of
said two frequencies in opposition and means
indicating the resultant eiîective energy.
6. In a course beacon system, a receiver includ
ing means for receiving impulse energy, iilter
could set his course at will with respect to the l0 means responsive to received impulse energy, said
given pulse interval at the transmitters, a pilot
fixed course by a mere manual adjustment of his
phase control means.
Alternately, in what would seem a far simpler
arrangement, appropriate adjustable phase dis
placement network means could ybe provided in
the output circuits of certain filters l1, i8, IS.
and 20. Calibrated adjustment of the phase of
one odd-multiple frequency with that of another
would serve to displace the b value at which a g'
or differential curve would have zero magnitude,
and hence enable a pilot to set his own course
with respect to a standard transmitted impulse
interval. The pilot could thus obtain readings
exactly as described in the foregoing and follow
his course as easily.
filter means comprising means for singling out
the fundamental, third, and ñfth harmonics of
the impulsing frequency of said received energy,
and indicating means responsive to Said singled
out frequency energy, said indicating means in
cluding means supplying the effective energy of
two of said frequencies in opposition and means
indicating the resultant effective energy.
7. In a course beacon system, a receiver accord
ing to claim 3, in which said ñlter means further
comprises means singling out energy of an even -
harmonic of the impulsing frequency of said re
ceived energy, and means indicating the effective
value of said even harmonic energy.
8. In a course beacon system, a receiver accord
ing to claim 3, in which said iilter means further
comprises means singling out energy of the sec
It might be mentioned with regard to the lat
ter forms of the invention that they are partic
ond harmonic of the impulsing frequency of said
ularly adaptable when it is desired to send a
number of bomber squadrons out on their mis
received energy, and means indicating the eiïec
sions simultaneously. Each pilot would then be 30 tive value of said second harmonic energy.
able to set his own course with respect to the
9. A course beacon system comprising a pair
beacon which may be used by all pilots.
of spaced antenna means, means supplying each
What is claimed is:
of said antenna means with impulse energy of
l. The method of guiding a mobile unit by sig
the same impulsing frequency, phase delay means
nals from a plurality of fixed spaced antennas 35 intermediate said supplying means and at least
which comprises generating energy in a periodi
one of said antenna means, whereby impulse
cally recurrent series of relatively short impulses,
energy emitted by one of said antenna means is
dividing such energy into a plurality of similar
phase displaced with respect to impulse energy
portions, introducing a relative delay between
emitted by the other of said antenna means, and
corresponding impulses in said portions, trans 40 receiver means responsive simultaneously to
mitting from each of said antennas energy from
energy emitted by both said antenna means, said
one of said portions, simultaneously receiving
receiver means including filter means responsiveY
to received impulse energy and singling out fre
energy radiated by each of said antennas, filter
quencies that are odd multiples of said impulsing
ing said received energy into individual odd
frequency and indicating means responsive to
multiple frequencies of said periodical recurrence,
two of said odd-multiple frequencies for indicat
and obtaining an indication of the relative mag
ing a characteristic of the received impulse
nitudes of the energy of two of said odd-multiple
energy, whereby a course indication may be
frequencies.
obtained.
2. The method of guiding a mobile unit which
10. A course beacon system comprising means
comprises transmitting from a pair of spaced 50
for transmitting from a ñrst fixed point energy
points energy in a periodically recurrent series
in a periodically recurrent series of relatively
of relatively short impulses, phase-displacing
short impulses, means for transmitting from a
impulse energy transmitted from one of said
second point spaced from said ñrst point similar
spaced points with respect to impulse energy
transmitted from the other of said spaced points, 55 impulse energy phase-displaced with respect to
energy transmitted from said first point, means
simultaneously receiving energy radiated from
for simultaneously receiving energy radiated
each of said spaced points, filtering said received
from each of said points, and means for obtain
energy into individual odd-multiple frequencies
ing an indication of the relative magnitudes of
of said periodical recurrence, and obtaining an
indication of the relative magnitudes of the 60 the energy of two frequency components of said
received impulse energy, said components being
energy of two of said odd-multiple frequencies.
odd multiples of said periodic recurrence.
3. In a course beacon system, a receiver includ
11. In a course beacon system, impulse generat
ing means for receiving impulse energy, filter
ing means, a pair of spaced antennas, phase de
means responsive to received impulse energy for
lay means responsive to energy from said impulse
singling out individual odd-harmonic components
generating means, means supplying energy from
of the impulse frequency, and indicating means
said impulse generating means to one of said an
responsive to two of said odd-harmonic compo
nents for indicating a characteristic of the re
tennas, means supplying energy from said phase
ceived impulse energy.
ing means for receiving impulse energy, ñlter
means responsive to received impulse energy for
delay means to the other of said antennas, re
ceiver means including iilter means responsive to
energy from each of said antennas, said filter
means singling out a frequency which is an odd
singling out individual odd-multiple frequencies
multiple of the impulsing frequency, and indicat
4. In a course beacon system, a receiver includ
of the period of said impulse energy, and indi
cating means responsive to two of said odd-mul
ing means responsive to the magnitude of said
75 odd-multiple frequency energy.
2,407,287
11
12
provide impulses of a time spaced relation from
said ñrst and said second points to provide a
course indication, and adjusting the amount of
tion from a íirst antenna and a second antenna
delay to obtain the time spaced relation from
having a predetermined ñxed spaced relationship
with respect to said course line, which comprises Cal the impulses required for course indication along
a selected one of said radial directions.
generating energy in a periodically recurring
12. A method of providing a beacon guiding
indication along a desired course line by radia
series of relatively short impulses, radiating said
14. In a beacon system for producing a course
energy from said íirst antenna over an area in
line by impulses of a predetermined time spaced
cluding the course line and said second antenna,
receiving the radiated energy at a point near said
relation according to a selected one of a plurality
of radial directions from a given radial center, a
ñrst antenna and a second antenna arranged in
second antenna, delaying the received energy,
radiating the delayed energy from said second
a predetermined ñxed spaced relation with respect
antenna over an area including said course line,
to said radial center, impulse generator means,
the delay being such as to produce a predeter
ñrst transmitter means for supplying energy from
mined time spaced relation between the impulses 15 said generator means to said Iirst antenna for
of the energy radiated from said ñrst antenna
and said second antenna along said course line,
receiving the transmitted pulse energy from both
radiation of impulses over a given area covering
distances considerably greater than the spacing
between said first and second antennas, receiver
means for receiving impulse energy from said
said first antenna and said second antenna at a
point within the radiation area of the tWo an-- 20 ñrst antenna, delay means connected to said re
tennas, and determining the position of said point
ceiver means, a second transmitter means con
relative to said course line by the difference in
nected between said delay means and said second
antenna for transmission of impulse energy from
the time spaced relation of the received impulse
said receiver over an area overlapping said given
energy from said predetermined time spaced rela
tion.
25 area, said delay means being adjustable to deter
mine the time spaced relation between the im
13. In a beacon system, the method of produc
pulses radiated from said ñrst antenna and said
ing a course line identiñed by impulses of a pre
second antenna, whereby said impulses indicate
determined time spaced relation according to a
selected one of a plurality of radial directions
for a given delay adjustment a selected course
from a given radial center, comprising generating 30 line in a radial direction with respect to said
radial center, receiver means for receiving im
energy in a periodically recurring series of rela
pulse energy from said first and said second an
tively short impulses, radiating said energy over
tennas, means in said receiver for determining the
a given area from a ñrst point spaced a predeter
time spaced relation of impulse energy received,
mined distance from said radial center, receivingr
the radiated energy at a second point spaced from 35 and means responsive to the time spaced rela- .
tion of the received impulse energy for indicating
said radial center and diametrically disposed with
the relative position of said receiver means with
respect to said ñrst point, delaying the received
respect to said selected course line.
energy, radiating the delayed energy from said
second point over the area including the area
covered by the radiation from said ñrst point to 40
EMILE LABIN.
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